Related papers: The Herman conjecture

In this paper, we study the persistence and remaining regularity of KAM invariant torus under sufficiently small perturbations of a Hamiltonian function together with its derivatives, in sense of finite smoothness with modulus of…

We study the statistical regularity of Mather measures associated with $C^1$ perturbations of a Tonelli Lagrangian. When the unperturbed Mather measure is supported on a quasi-periodic torus with a Diophantine frequency, we establish…

We prove a Montel theorem for Hilbert space valued functions, and a non-commutative version of this theorem, by composing with unitaries to achieve convergence.

In this paper, the Conley conjecture, which were recently proved by Franks and Handel \cite{FrHa} (for surfaces of positive genus), Hingston \cite{Hi} (for tori) and Ginzburg \cite{Gi} (for closed symplectically aspherical manifolds), is…

We initiate a general quantitative study of sets of $\mathcal{M}$-points, which are special subsets of rational points, generalizing Campana points, Darmon points, and squarefree solutions of Diophantine equations. We propose an asymptotic…

We apply KAM theory to the equation of the forced relativistic pendulum to prove that all the solutions have bounded momentum. Subsequently, we detect the existence of quasiperiodic solutions in a generalized sense. This is achieved using a…

We show that if $\mathcal{L}$ is a line in the plane containing a badly approximable vector, then almost every point in $\mathcal{L}$ does not admit an improvement in Dirichlet's theorem. Our proof relies on a measure classification result…

We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…

In this paper we discuss dilaton shifts (Euler counterterms) arising in decomposition of two-dimensional quantum field theories with higher-form symmetries. These take a universal form, reflecting underlying (noninvertible, quantum)…

This paper investigates in depth how stochastic perturbations affect the integrable structure of Hamiltonian systems and develops a KAM theory for stochastic Hamiltonian dynamics, in the sense of the most probable path. We first derive the…

Consider a real--analytic nearly--integrable mechanical system with potential $f$, namely, a Hamiltonian system, having a real-analytic Hamiltonian $$ H(y,x)=\frac12 | y |^2 +\e f(x)\ , $$ $y,x$ being $n$--dimensional standard action--angle…

In the paper the well known Riemann Hypothesis is proven. The proof is based on uniform approximation of the zeta function discs of the critical strip placed to the right from the critical line.The basic moment is a use of a new mesure…

We prove a multidimensional weighted analogue of the well-known theorem of Kurzweil (1955) in the metric theory of inhomogeneous Diophantine approximation. Let $A$ be matrix of real numbers, $\Psi$ an $n$-tuple of monotonic decreasing…

We prove that for any compact toric symplectic manifold, if a Hamiltonian diffeomorphism admits more fixed points, counted homologically, than the total Betti number, then it has infinitely many simple periodic points. This provides a vast…

The famous hoop conjecture by Thorne has been claimed to be\ violated in curved spacetimes coupled to linear electrodynamics. Hod \cite{Hod:2018} has recently refuted this claim by clarifying the status and validity of the conjecture…

This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport's problem regarding badly approximable points on submanifolds of a Euclidean space and Schmidt's problem regarding the intersections of…

We give a new proof the arithmetic Hilbert-Samuel theorem by using classical reductions in the theory of coherent sheaves, a direct proof in the case of the projective space and the conservation of some numerical invariants, called…

We show that an earlier conjecture of the author, on diophantine approximation of rational points on varieties, implies the ``abc conjecture'' of Masser and Oesterl'e. In fact, a weak form of the former conjecture is sufficient, involving…

We prove a conjecture of Lehmann-Tanimoto about the behaviour of the Fujita invariant (or $a$-constant appearing in Manin's conjecture) under pull-back to generically finite covers. As a consequence we obtain results about geometric…

Let us denote by $\mathcal K_n$ the hyperspace of all convex bodies of $\mathbb R^n$ equipped with the Hausdorff distance topology. An affine invariant point $p$ is a continuous and Aff(n)-equivariant map $p:\mathcal K_n\to \mathbb R^n$,…